Finite Element Method Explained in 3 Levels of Difficulty

The finite element method is difficult to understand when studying all of its concepts at once. Therefore, I explain the finite element method in three levels with increasing complexity. At each level, different shape functions are introduced for discretizing the solution function of the given differential equation. At the first level, the shape functions are defined globally. At the second level, the shape functions are defined at the element level. And at the third level, the shape functions are defined on a reference element. Along the way, the concepts of assembly, integration by substitution and Gaussian quadrature are explained.

Video about the weak formulation:    • I finally understood the Weak Formula...  

This is my contribution to the Summer of Math Exposition (SoME). You can support me by joining the competition as a judge until August 18: https://some.3b1b.co/

0:00 Introduction
2:45 Level 1
19:37 Level 2
26:33 Level 3
38:21 Summary

Keywords: finite element method, finite element analysis, partial differential equation, Poission problem, weak formulation, discretization, assembly, isoparametric concept, reference element, Gaussian quadrature

Music: Swans In Flight - Asher Fulero